4th International Conference on
Earthquake Geotechnical Engineering
June 25-28, 2007
Paper No. 1640
ANALYTICAL VERIFICATION OF BURIED STEEL PIPELINES AT
STRIKE-SLIP FAULT CROSSINGS
Dimitriοs KARAMITROS1, George BOUCKOVALAS2, and George KOURETZIS3
ABSTRACT
Existing analytical methods for the stress analysis of buried steel pipelines at crossings with active
strike-slip faults depend on a number of simplifications, which limit their applicability and may even
lead to non-conservative results. The analytical methodology presented herein maintains the wellestablished assumptions of existing methodologies, but also introduces a number of refinements in
order to achieve a more wide range of application without any major simplicity sacrifice. More
specifically, it employs equations of equilibrium and compatibility of displacements to derive the axial
force applied on the pipeline and adopts a combination of beam-on-elastic-foundation and elasticbeam theory to calculate the developing bending moment. Although indirectly, material and largedisplacement non-linearities are also taken into account, while the actual distribution of stresses on the
pipeline cross-section is considered for the calculation of the maximum design strain.
Keywords: buried steel pipelines, strike-slip faults, stress analysis, design
INTRODUCTION
Evaluation of the response of buried steel pipelines at active fault crossings is among their top seismic
design priorities. This is because the axial and bending strains induced to the pipeline by step-like
permanent ground deformation may become fairly large and lead to rupture, either due to tension or
due to buckling. Apart from the detrimental effects that such a rupture can have to the operation of
critical lifeline systems (EERI, 1999, Uzarski and Arnold, 2001), an irrecoverable ecological disaster
may also result from the leakage of environmentally hazardous materials such as natural gas, fuel or
liquid waste.
A simplified methodology which is widely used today for strike-slip and normal faults, is the one
originally proposed by Kennedy et al. (1977), and consequently adopted by the ASCE (1984)
guidelines for the seismic design of pipelines. Kennedy et al. extended the pioneering work of
Newmark & Hall (1975), by taking into account soil-pipeline interaction in the transverse, as well as
in the longitudinal direction. Their methodology applies to cases where the fault rupture provokes
severe elongation of the pipeline, so as tension is the prevailing mode of deformation.
Wang & Yeh (1985) tried to overcome this shortcoming by taking the pipeline bending stiffness into
account. Their methodology refers only to strike-slip faults and relies on partitioning of the pipeline
into four (4) distinct segments: two (2) in the high curvature zone on both sides of the fault trace, and
another two (2) outside this zone. The latter segments are treated as beams-on-elastic-foundation,
1
Department of Geotechnical Engineering, School of Civil Engineering, National Technical
University of Athens, Greece, Email: dimkaram@central.ntua.gr
2
Professor, Department of Geotechnical Engineering, School of Civil Engineering, National Technical
University of Athens, Greece, Email
3
Department of Geotechnical Engineering, School of Civil Engineering, National Technical
University of Athens, Greece
while the former ones are assumed to deform as circular arcs, with a radius of curvature calculated
from the equations of equilibrium and the demand for continuity between adjacent segments. Although
clearly advanced, compared to the methodology of Kennedy et al. (1977), the methodology of Wang
and Yeh also features two main pitfalls, which may lead to non-conservative predictions: (a) the most
unfavorable combination of axial and bending strains along the pipeline is assumed to develop outside
the high-curvature zone and (b) the effect of axial tension on the pipeline’s bending stiffness is
overlooked.
METHODOLOGY OUTLINE
In summary, the proposed methodology computes axial and bending strains along the pipeline with the
aid of beam-on-elastic-foundation and elastic-beam theories, taking into account the bending stiffness
of the pipeline cross-section, as well as the soil-pipeline interaction effects in both the axial and the
transverse directions. Material non-linearity is considered by assuming a bilinear stress-strain
relationship for the pipeline steel, combined with an iterative linear elastic solution scheme which uses
the secant Young’s modulus of the pipeline steel in order to ensure compatibility between computed
non-linear stresses and strains.
Lc
Lc
A'
∆x
A
β
∆y
B
C
pipeline
q(x) = - k w(x)
C'
fault
Lc
A
x
w
qu
δ=∆y/2
A'
Cr
δ=∆y/2
B
qu
Cr
w
x
C
Lc
C'
q(x) = - k w(x)
Figure 1. Partitioning of the pipeline into 4 segments
b.
q(x) = - k w(x)
x
φA
VA
A
A'
w
MA
Lc
Cr
MA
φA
A
VA
qu
Figure 2. Analysis model for pipeline segments (a) AA´ (b) AB
B
δ=∆y/2
a.
The strike-slip fault is taken as an inclined plane, i.e. with null thickness of rupture zone, so that the
intersection of the pipeline axis with the fault trace on the ground surface is reduced to a single point.
The fault movement is defined in a Cartesian coordinate system, where the x-axis is collinear with the
undeformed longitudinal axis of the pipeline, while the y-axis is perpendicular to x in the horizontal
plane. Subsequently, the fault movement is analyzed into two Cartesian components, ∆x and ∆y,
interrelated through the angle formed by the x-axis and the fault trace. In its present form, the
proposed method applies to crossing angles β ≤ 90° , resulting in pipeline elongation.
Following the general concept originally introduced by Wang & Yeh (1985), the pipeline is
partitioned into four (4) segments, defined by the characteristic points A, B and C in Figure 1: Point B
is the intersection of the pipeline axis with the fault trace, while points A and C are the closest points
of the pipeline axis with zero y displacement. The computation of combined axial and bending
pipeline strains can be broken down into six (6) steps, briefly presented in the following. The detailed
methodology workflow can be found in Karamitros et al. (2006), while a computer code for the
application of the methodology can be downloaded from:
http://users.civil.ntua.gr/gbouck/en/publications.htm .
As in all similar design methodologies (Newmark and Hall, 1975, Kennedy et al., 1977, Wang and
Yeh, 1985), the solution algorithm overlooks initial pipeline stresses due to soil overburden, as they
are fairly small compared to the ones developing due to fault movement. Furthermore, pipeline and
soil inertia effects are not taken into account as the velocity of the sliding part of the fault is
considered to be sufficiently small, while concurrent spatially variable transient motion is neglected in
the computations. Finally, it should be stressed that the proposed methodology overlooks local
buckling and section deformation effects (Calladine, 1983), two phenomena which dominate pipeline
behavior at large fault displacements. As a result, its application range is limited within the allowable
strains which are explicitely defined by design codes (e.g. ALA-ASCE, 2005, CEN, 2003) in order to
avoid such detrimental effects. For larger strain levels, rigorous numerical methods, or large
displacement approximate methods (e.g. Takada et al., 2001) should be used.
Step 1
Segments AA´ and CC´ are analyzed as beams-on-elastic-foundation in order to obtain the relation
between shear force, bending moment and rotation angle at points A and C. More specifically, setting
w = 0 for x = 0 and w → 0 for x → ∞ in the differential equilibrium equation E1Iw ′′′′ + kw = 0 for
the elastic line of segment AA´ (Figure 1), yields:
w = Ce −λx sin λx
(1a)
where:
λ=
4
k
4E1I
(1b)
x is the distance from point Α along the pipeline axis, w is the transverse horizontal displacement, E1
is the elastic Young’s modulus of the pipeline steel, Ι is the moment of inertia of the pipeline crosssection, and k is the constant of the transverse horizontal soil springs (Figure 2a). According to the
ALA-ASCE (2005) guidelines, computation of k can be based on Hansen (1961) and Trautmann &
O'Rourke (1983).
Differentiation of Eq. (1a) yields the following relations between the shear force VA = − E1I ⋅ w ′′′
A , the
bending moment M A = − E1I ⋅ w ′′A and the rotation φA = w ′A at point Α:
M A = ( 2λE1I ) ⋅ φA
(2)
VA = −λ ⋅ M A
(3)
Due to symmetry, similar relations apply for point C.
Step 2
Considering the boundary conditions determined in Step 1, segments AB and BC are analyzed with
the elastic-beam theory, in order to derive the maximum bending moment M max . Due to symmetry,
the analysis can be focused on segment AB. This segment is modeled as an elastic beam, supported at
point Α by a rotational spring, whose constant is calculated from Eq. (2) as C r = 2λE1I , and at point B
by a joint, which is displaced by half the transverse component of the strike-slip fault movement, i.e.
δ = ∆y 2 . As a result, a uniformly distributed load q u is applied to the beam, equal to the limit value
of soil reaction for transverse horizontal movement of the pipeline relatively to the surrounding soil
(Figure 2b). According to the ALA-ASCE (2005) guidelines, the value of q u can be calculated from
the properties of the backfill of the pipeline trench, based on the relations proposed by Hansen (1961)
and Trautmann & O'Rourke (1983).
Application of the elastic-beam theory yields the following bending moment and shear force reactions
on the supports A and B:
24EIδC r − q u Cr L4c
24EILc + 8C r L2c
(4)
VA =
24EIδC r − 12EIq u L3c − 5q u Cr L4c
24EIL2c + 8Cr L3c
(5)
VB =
24EIδC r + 12EIq u L3c + 3q u Cr L4c
24EIL2c + 8Cr L3c
(6)
MA =
Eqs. (4)-(6) express the reaction forces of segments AB and BC in terms of the curved length L c of
the beam, which is not a priori known. However, substituting Eqs. (4) and (5) into Eq. (3) yields:
a 5 L5c + a 4 L4c + a 3 L3c − a1Lc − a 0 = 0
(7)
where a 0 to a 5 are known constants, equal to a 0 = 24EIδC r , a1 = 24EIδC r λ , a 3 = 12EIq u , a 4 = 5q u C r
and a 5 = q u C r λ .
The above polynomial equation can be solved iteratively, using the Newton-Raphson method, with a
large initial value for L c (e.g. 500m). In this way, the values of M A , VA , and VB can be directly
estimated, and the maximum bending moment developing on the pipeline can be consequently
calculated from the elastic-beam theory, as:
M max =
3VB 2
x max
2q u
(8)
Step 3
Similar to all existing methodologies (Newmark and Hall, 1975, Kennedy et al., 1977, Wang and Yeh,
1985), the axial force at the intersection of the pipeline with the fault trace is calculated from the
requirement for compatibility between the geometrically required and the stress-induced (available)
pipeline elongation. The required elongation ∆L req is defined as the elongation imposed to the
pipeline due to the fault movement. For the sake of simplicity, the elongation provoked by the ∆y fault
displacement component may be neglected, as it is minimal compared to the elongation due to the ∆x
component. Therefore:
∆L req ≈ ∆x
(9)
On the other hand, the available elongation ∆L av is defined as the elongation resulting from the
integration of axial strains along the unanchored length, i.e. the length over which slippage occurs
between the pipeline and the surrounding soil:
Lanch
∆L av = 2
∫ ε ( L ) ⋅ dL
(10)
0
where L is the distance from the fault trace, while the factor 2, by which the integral in Eq. (10) is
multiplied, accounts for the elongation on both sides of the fault trace.
The unanchored length L anch may be calculated from the equilibrium along the pipeline axis, assuming
that axial pipeline stresses essentially become zero at the far end of the unanchored length. In this way,
L anch is expressed as:
Lanch =
Fa σa As
=
tu
tu
(11)
where Fa and σ a are the axial force and stress developing in the intersection of the pipeline axis with
the fault trace, A s is the area of the pipeline cross-section and t u is the limit friction due to the
slippage of the pipeline relatively to the surrounding soil (ALA-ASCE, 2005).
The distribution of strains along the unanchored length can be consequently derived from the
corresponding stresses, assuming a bilinear stress-strain relationship for the pipeline steel. Assuming
further that axial stresses attenuate linearly with the distance from the fault trace, due to the constant
value of the limit friction force, tensile stresses along the pipeline axis can be expressed as:
σ ( L ) = σa −
tu
L
As
(12)
For the case where the axial tensile stress σ a is below the yield limit σ1 , Eq. (10) can be re-written as:
Lanch
∆L av = 2
∫
0
σ(L)
E1
⋅ dL =
σa2 A s
E1 t u
(13)
Therefore, for ∆Lav = ∆L req , the maximum tensile stress becomes:
σa =
E1 t u ∆L req
As
If the required elongation is larger than the one corresponding to σ a = σ1 , i.e. when:
(14)
∆L req >
σ12 A s
E1 t u
(15)
then plastic strains develop in the pipeline and Eq. (10) becomes:
Lanch
⎡ L1 ⎛
⎤
σ ( L ) − σ1 ⎞
σ ( L)
∆Lav = 2 ⎢ ∫ ⎜ ε1 +
⋅ dL ⎥
⎟ ⋅ dL + ∫
E2
E1
⎢⎣ 0 ⎝
⎥⎦
⎠
L1
(16)
where:
L1 =
( σa − σ1 ) A s
(17)
tu
Combining Eq. (11), (12), (16) and (17), the maximum developing tensile stress becomes:
σ1 ( E1 − E 2 ) + σ12 ( E 22 − E1E 2 ) + E12 E 2 ∆L req
σa =
tu
As
E1
(18)
Regardless of the axial stress level, the corresponding axial force is equal to:
Fa = σa A s
(19)
Step 4
According to the elastic beam theory, bending strains on the pipeline can be calculated as:
ε Ib =
M max D
2EI
(20)
where D is the external pipeline diameter.
The above equation is accurate for small fault displacements, while for larger fault displacements,
geometrical second-order effects must be also taken into account. To simplify this relatively complex
problem, the bending stiffness of the pipeline may be approximately neglected (Kennedy et al., 1977),
so that bending strains can be computed geometrically as:
ε IIb =
D
2
R
(21)
The radius of curvature R results from the equilibrium of the forces acting on an infinitesimal part of
the pipeline’s curved length:
R=
Fa
qu
(22)
qu D
2Fa
(23)
and finally:
ε IIb =
Eq. (23) indicates that bending strains induced by second-order effects are inversely proportional to
the axial force applied on the pipeline. In other words, for small fault displacements, bending strains
computed by Eq. (23) tend to become infinite. This is due to the fact that Eq. (22) has been derived
assuming that the pipeline bending stiffness is equal to zero, which is approximately true only when
the whole pipeline cross-section is under yield.
According to the above, the actual bending strain ε b lays between εIb and εIIb , asymptotically
approaching ε Ib as fault displacements tend to zero and εIIb in the opposite case. Here, it is
approximately assumed that:
1
1 1
= I + II
εb εb εb
(24)
Step 5
Existing methodologies (Newmark and Hall, 1975, Kennedy et al., 1977, Wang and Yeh, 1985)
calculate the axial strain directly from the axial stress, using the adopted stress-strain relation for the
pipeline steel. When strains in the pipeline cross-section remain in the elastic range, this assumption is
valid for every point along the pipeline axis. However, when yielding occurs, it is accurate only at the
intersection of the pipeline with the fault trace, where the bending strain is zero. In the vicinity of the
cross-section where the maximum bending strain occurs, axial strain increases locally, so that the
integral of stresses on the pipeline cross-section remains equal to the applied axial force.
In the present work, the interaction between axial and bending strains is quantified by determining the
exact distribution of strains and stresses on the pipeline cross-section. For this purpose, the beamtheory assumption of plane cross-sections is embraced, while the stress-strain curve of the pipeline
steel is considered to be bilinear.
εmax=εa+εb
θ
σmax
ε1
σ1
εa
φ1
σa
π-φ2
-ε1
εmin=εa-εb
-σ1
σmin
Figure 3. Non-linear stress and strain distribution on the pipeline cross-section
Bearing in mind the above, the strain distribution on the cross-section is given by Eq. (25):
ε = ε a + ε b cos θ
(25)
where the angle θ is the polar angle of the cross-section, defined in Figure 3. The corresponding
distribution of stresses on the pipeline cross-section is given by Eq. (26):
0 ≤ θ < φ1
⎧ σ1 + E 2 ( ε − ε1 )
⎪
E1ε
σ=⎨
φ1 ≤ θ ≤ π − φ2
⎪−σ + E ( ε + ε ) π − φ < θ ≤ π
2
1
2
⎩ 1
(26)
where the angles φ1,2 define the portion of the cross-section that is under yield (Figure 3), and are
calculated as:
φ1,2
ε1 ∓ ε a
⎧
π
< −1
⎪
εb
⎪
⎪⎪
⎛ε ∓ε ⎞
ε ∓ε
= ⎨arccos ⎜ 1 a ⎟ −1 ≤ 1 a ≤ 1
εb
⎝ εb ⎠
⎪
⎪
ε ∓ε
⎪
0
1< 1 a
εb
⎪⎩
(27)
The total axial force is calculated by integrating the stresses over the cross-section, as:
π
F = 2 ∫ σR m tdθ ⇒
0
⎡ E1πε a − ( E1 − E 2 )( φ1 + φ2 ) ε a +
⎤
F = 2R m t ⋅ ⎢
⎥
⎣⎢( E1 − E 2 )( φ1 − φ2 ) ε1 − ( E1 − E 2 )( sin φ1 − sin φ2 ) ε b ⎦⎥
(28)
where:
Rm =
D−t
2
(29)
The axial strain of the pipeline can be derived from the demand for equilibrium, by equating the axial
force computed using Eq. (28), to the one calculated using Eq. (19). Note that Eq. (19) applies strictly
at the pipeline’s intersection with the fault trace, but it is approximately extended to the neighboring
position of the maximum bending moment. The solution of the system of Eqs. (27) and (28) results in
a complex formula for ε a , which can be solved iteratively, using the Newton-Raphson method and
starting from an initial value of ε0a = 0 .
Having calculated the axial strain at the position of maximum bending strain, the minimum and
maximum longitudinal strains can be subsequently computed as their algebraic sum (i.e.
ε max,min = εa ± ε b ).
Step 6
The analysis of segments AB and BC, from which the maximum bending moment emerges, is based
on the elastic beam theory and is not taking into account the non-linear behavior of the pipeline steel.
Since the steel stress-strain relationship is considered to be bilinear, a series of equivalent linear
calculation loops is performed, employing a procedure for readjusting the secant Young’s modulus of
the pipeline steel on each loop.
More specifically, using the already defined stress distribution on the pipeline cross-section, the
corresponding bending moment can be calculated using Eq. (30):
π
M = 2 ∫ σR m tR m cos θdθ ⇒
0
⎡ E1πε b
⎤
⎢ 2 − ( E1 − E 2 )( sin φ1 − sin φ2 ) ε a + ( E1 − E 2 )( sin φ1 + sin φ 2 ) ε1 ⎥
⎥
M = 2R m 2 t ⋅ ⎢
⎢ ( E1 − E 2 )( φ1 + φ2 ) ε b ( E1 − E 2 )( sin 2φ1 + sin 2φ2 ) ε b
⎥
−
⎢⎣ −
⎥⎦
2
4
(30)
Therefore, the secant modulus for the next iteration can be calculated as:
E′sec =
M ( εa , εb ) ⋅ D
2Iε
I
b
=
M ( εa , εb ) ⋅ D ⎛ 1 1 ⎞
⎜ − II ⎟
2I
⎝ εb εb ⎠
(31)
and Steps 2 to 6 are repeated, until convergence is accomplished.
VALIDATION OF THE PROPOSED METHODOLOGY
To validate the results of the proposed methodology, analytical predictions are compared to the results
from a series of 3-D non-linear numerical analyses with the Finite Element Method, performed with
the commercial code MSC/NASTRAN (The MacNeal – Schwendler Corporation, 1994). For this
purpose, a typical high-pressure natural gas pipeline was considered, featuring an external diameter of
0.9144m (36in), a wall thickness of 0.0119m (0.469in), and a total length of 1000m. A hybrid model
was used for the simulation of the pipeline, with a part of 50m along both sides of the fault trace (i.e. a
total length of 100m) modeled as a cylindrical shell, and the remaining 450m part (i.e. a total length of
900m) modeled as a beam (Figure 4). The shell perimeter was discretized into 16 equal sized
quadrilateral shell elements, each of 0.20m length. The beam part was discretized with 0.50m long
beam elements. The pipeline steel was of the API5L-X65 type, with a bilinear elasto-plastic stressstrain curve and the properties listed in Table 1.
To simulate soil-pipeline interaction effects, each node of the model was connected to axial, transverse
horizontal and vertical soil springs, modeled as elastic-perfectly plastic rod elements. The properties of
the soil-springs (Table 3) were calculated according to the ALA-ASCE (2005) guidelines, assuming
that the pipeline top is buried under 1.30m of medium-density sand with friction angle φ=36º and unit
weight γ=18kΝ/m2. The fault movement was applied statically at the sliding part of the fault, as a
permanent displacement of the free end of the corresponding soil-springs.
Table 1: API5L-X65 steel properties considered in the numerical analyses
Yield stress (σ1)
490MPa
Failure stress (σ2)
531MPa
Failure strain (ε2)
4.0%
Elastic Young’s modulus (Ε1)
210GPa
Yield strain ( ε1 = σ1 E1 )
0.233%
Plastic Young’s modulus ( E 2 = ( σ2 − σ1 ) ( ε 2 − ε1 ) )
1.088GPa
Table 2: Soil spring properties considered in the numerical analyses
Yield force
Yield displacement
Axial (friction) springs
40.5 kN/m
3.0 mm
Transverse horizontal springs
318.6 kN/m
11.4 mm
Vertical springs (upward movement)
52.0 kN/m
2.2 mm
Vertical springs (downward movement)
1360.0 kN/m
100.0 mm
Shell elements
Rigid element
Beam elements
Axial soil springs
Horizontal soil springs
Vertical soil springs
Figure 4. 3-D model used for analyses with the Finite Element Method: the junction between
shell and beam part
3
2
εb (%)
Kennedy et al. (1977)
Wang & Yeh (1985)
Proposed Method
Numerical
1
2
1
0
0
3
3
2
2
εmax (%)
εa,max (%)
εa,fault (%)
3
1
0
1
0
0
0.5
1
∆f / D
1.5
2
0
0.5
1
∆f / D
1.5
2
Figure 5. Comparison of the results of the proposed analytical methodology with the results of
the numerical analyses and the predictions of the Kennedy et al. (1977) and Wang & Yeh (1985)
methods
Considering the intersection angle between the fault trace and the pipeline axis to be equal to β = 45 ,
the analysis proceeded incrementally to a final fault displacement ∆f = 2D . Results from analyses for
different angles β are presented in Karamitros et al. (2006).
The numerical results are presented in Figure 5 in comparison with analytical predictions according to
the proposed methodology, as well as the methodologies of Kennedy et al. (1977) and Wang & Yeh
(1985). The top left graph of Figure 5 shows the comparison between analytical and numerical
predictions of axial strain εa,fault at the pipeline-fault trace intersection. The agreement appears fairly
good, for all analytical methods. As the main assumption for computing ε a,fault is the compatibility
between the geometrically required and the stress induced (available) elongation of the pipeline, the
observed agreement is essentially considered as a solid verification of this assumption.
The bottom left graph of Figure 5 refers to the overall maximum axial strain εa,max , which does not
necessarily develop at the pipeline-fault trace intersection, as the existing analytical methods imply. In
this case, a good overall agreement is observed only between numerical results and analytical
predictions with the proposed methodology. The existing analytical methods approach the numerical
solution at large displacements, after the yield strain of the pipeline steel has been exceeded, while
they grossly under-predict εa,max at smaller displacements. Note that observed differences are larger at
intermediate displacement levels, of the order of ∆f ≈ 1D , which are commonly encountered in
practice.
Focusing next on bending strains ε b (top right graph of Figure 5), a good overall agreement is
observed again between the proposed analytical method and the numerical analyses. The Kennedy et
al. (1977) method proves accurate in the region of large displacements ( ∆f D > 1.5 ), i.e. when the
criteria for the applicability of the method are met, but seriously over-predicts ε b for smaller fault
displacements. The Wang & Yeh (1985) method under-predicts ε b for the entire range of fault
displacements analyzed herein, mainly because it neglects the effect of axial tension on the pipeline
bending stiffness.
The maximum longitudinal strains ε max = ε a,max + ε b are probably the best criterion for the evaluation
of the proposed methodology, as they form the basis of pipeline design. From the bottom right graph
of Figure 5, it may be observed that the good overall performance of the proposed method,
acknowledged in the previous comparisons, applies here as well. As expected, the Kennedy et al.
(1977) method over-predicts maximum strains for small fault displacements. This trend is reversed at
intermediate levels of fault displacement, and the divergence is gradually reduced as displacements
increase. Finally, the methodology of Wang & Yeh (1985) provides accurate results only in the region
of large displacements, where axial tension is the prevailing mode of deformation. For small and
intermediate fault displacements ε max is consistently under-estimated.
CONCLUSION
An improved analytical methodology has been developed for the stress analysis of buried steel
pipelines crossing active strike-slip faults. It is based on firm assumptions adopted in the existing
analytical methodologies of Kennedy et al. (1977) and Wang & Yeh (1985), but proceeds further:
• to analyze the curved part of the pipeline with the aid of elastic-beam theory, in order to locate
the most unfavorable combination of axial and bending strains, and
• to consider the actual stress distribution on the pipeline cross-section, in order to account for the
effect of curvature on axial strains and calculate the design maximum strain.
Acknowledging that there is no end to the refinements that can be applied to simplified analytical
methodologies, it needs to be stressed out that the above modifications considerably improve the
accuracy of analytical predictions, especially for small and medium fault displacements, while they
still permit a simple analytical solution algorithm to be developed. In fact, although more complicated
than the most commonly used today method of Kennedy et al. (1977), the computational algorithm of
the proposed methodology remains relatively simple and stable, and can be easily programmed for
quick application.
Note that, in its present form, the proposed method applies to intersection angles β ≤ 90° resulting in
elongation of the pipeline. Furthermore, it does not account for the effects of local buckling and
section deformation. Therefore, its application should not be extended beyond the strain limits
explicitely defined by design codes in order to mitigate such phenomena.
ACKNOWLEDGEMENTS
This research is supported by the “EPEAEK II Pythagoras” grant, co-funded by the European Social
Fund (75%) and the Hellenic Ministry of Education (25%).
REFERENCES
American Lifelines Alliance – ASCE. Guidelines for the Design of Buried Steel Pipe, July 2001 (with
addenda through February 2005).
ASCE Technical Council on Lifeline Earthquake Engineering. Differential Ground Movement Effects
on Buried Pipelines. Guidelines for the Seismic Design of Oil and Gas Pipeline Systems, 150-228,
1984.
Calladine CR. Theory of Shell Structures, Cambridge, Cambridge University Press, 1983.
CEN European Committee for Standardisation. Eurocode 8: Design of structures for earthquake
resistance, Part 4: Silos, tanks and pipelines, Draft No 2, Ref. No. EN1998-4: 2003 (E), December
2003.
EERI. The Izmit (Kocaeli), Turkey Earthquake of August 17, 1999. EERI Special Earthquake Report,
1999.
Hansen JB. The Ultimate Resistance of Rigid Piles Against Transversal Forces. Bulletin 12. Danish
Geotechnical Institute, Copenhagen, Denmark, 1961.
Karamitros DK, Bouckovalas GD, and Kouretzis GP. “Stress analysis of buried steel pipelines at
strike-slip fault crossings,” Soil dynamics and Earthquake Engineering, doi:10.1016/
j.soildyn.2006.08.001, 2006.
Kennedy RP, Chow AW, and Williamson RA. “Fault Movement Effects on Buried Oil Pipeline,”
Transportation Engineering Journal, ASCE, 103, 617-633, 1977.
Newmark NM and Hall WJ. “Pipeline Design to Resist Large Fault Displacement,” Proceedings of the
U.S. National Conference on Earthquake Engineering. Ann Arbor, University of Michigan, 416425, 1975.
Takada S, Hassani N, and Fukuda K. “A New Proposal for Simplified Design of Buried Steel Pipes
Crossing Active Faults,” Earthquake Engineering and Structural Dynamics, 30, 1243-1257, 2001.
The MacNeal - Schwendler Corporation. MSC/NASTRAN for Windows: Reference Manual, 1994.
Trautmann CH and O'Rourke TD. Behavior of Pipe in Dry Sand Under Lateral and Uplift Loading.
Geotechnical Engineering Report 83-6. Cornell University, Ithaca, New York, 1983.
Uzarski J and Arnold C. “Chi-Chi, Taiwan, Earthquake of September 21, 1999, Reconnaissance
Report,” Earthquake Spectra, The Professional Journal of the EERI, 17(Supplement A), 2001.
Wang LRL and Yeh Y. “A Refined Seismic Analysis and Design of Buried Pipeline for Fault
Movement,” Earthquake Engineering and Structural Dynamics, 13, 75-96, 1985.